Volume of a Sphere

Q.

Three spheres of radii $3cm,4cm,5cm$ respectively are melted together to form a single solid sphere. Find the radius of the resulting sphere.

1. $5.02cm$

2. $2.21cm$

3. $6cm$

4. $6.22cm$

Q. The radius of the sphere is given to be $5\text{cm}$. What will be the volume of this sphere?

1. $\frac{100}{3}\pi {\text{cm}}^3$
2. $\frac{500}{3}\pi {\text{cm}}^3$
3. $500\pi {\text{cm}}^3$

Q. Plastic drum of cylindrical shape is made by melting spherical solid plastic balls of radius 1cm . Find the number of balls required to make the drum of thickness 2 cm , height is 90 cm and outer radius is 30 cm . ( Drum has no led)

Q. What is the surface area of a sphere whose radius is $6$ units and what is the volume of the sphere?

1. Surface area of the sphere $=144\pi uni{t}^2$
   Volume of the Sphere $=144\pi uni{t}^3$
2. Surface area of the sphere $=144\pi uni{t}^2$
   Volume of the Sphere $=288\pi uni{t}^3$
3. Surface area of the sphere $=288\pi uni{t}^2$
   Volume of the Sphere $=144\pi uni{t}^3$
4. Surface area of the sphere $=288\pi uni{t}^2$
   Volume of the Sphere $=288\pi uni{t}^3$

Q.

How many spherical lead shots, each of radius $1\mathrm{cm}$ can be made from a sphere of radius $4\mathrm{cm}$ ?

1. $32$

2. $16$

3. $64$

4. $48$

Q. 35. The radius of the base of a right circular cylinder is increased by 75% and the height is decreased by 50% . Find the percent increase or decrease in the volume

Q. A figure of sphere is given below:


Find the volume of this sphere.

1. $4000\pi {\text{cm}}^3$
2. $1333.33\pi {\text{cm}}^3$
3. $133.33\pi {\text{cm}}^3$
4. $10666.67\pi {\text{cm}}^3$

Q. The area of the circle is $154{\text{cm}}^2$. If the radius of the sphere is same as the radius of the circle, then what will be the volume of the sphere?

NOTE: Take the value of $\pi =\frac{22}{7}$

1. $1437.33{\text{cm}}^3$
2. $205.33{\text{cm}}^3$
3. $4312{\text{cm}}^3$
4. $1437.33{\text{cm}}^2$

Q.

A balloon that always remains spherical has a variable radius.

The rate at which its volume is increasing is $m\pi c{m}^2$ with the radius when the latter is $10cm$.

Find $m$.

Q.

Two solid cones, A and B, are placed in a cylindrical tube as shown in the given figure. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder. [Assume the thickness of the cones to be negligible.]

1. $386\text{cubic units}$
2. $396\text{cubic units}$
3. $376\text{cubic units}$
4. $406\text{cubic units}$

Q.

How many coins of radius 1 cm and thickness 0.28 CM should be melted to form a solid cylinder of height 7 cm and diameter 8 cm

Q.

Find the values of m and n if:

$4^{2m}=(\sqrt[3]{316}{)}^{-\frac{6}{n}}=(\sqrt{8}{)}^2$

Q. The inner diameter of a cylindrical wooden pipe is 24cm and its outer diameter is 28 cm. The length of the pipe is 35cm.Find the mass of the pipe, if 1cm³ of wood has a mass of 0.6g.

Q.

Question 107

Metallic discs of radius 0.75 cm and thickness 0.2 cm are melted to obtain 508.68 $c{m}^3$ of metal. Find the number of disc melted. (Use $\pi =3.14$)

Q. How many small cubes of edge length 2 cm each can be accommodated in a cubical box with edge length 6 cm?

1. 15
2. 18
3. 27
4. 21

Q. If the radius of a sphere increases from $4\text{cm}$ to $7\text{cm}$, then what is the difference between the volume of both the spheres ?

1. $\frac{1327}{3}\pi$
2. $\frac{1071}{3}\pi$
3. $\frac{1583}{3}\pi$
4. None of the above.

Q. Find the volume of the sphere whose curved surface area is $616{cm}^2$.

Q. One solid hemisphere melted into solid sphere, then what is the ratio of radius of solid sphere hemisphere ?

1. $\sqrt[3]{32}$ : 1
2. 1 : $\sqrt[3]{32}$
3. 8 : 1
4. 1 : 8

Q. Mary serves juice to her guests in cylindrical cups of radius 7 cm having a height of 10 cm. If she serves 25 cups, she will need cm${}^3$ of juice.

1. 1540
2. 3850
3. 77000
4. 38500